This paper proposes an evolutionary Rao algorithm (ERA) to enhance three state-of-the-art metaheuristic Rao algorithms (Rao-1, Rao-2, Rao-3) by introducing two new schemes. Firstly, the population is split into two sub-populations based on their qualities: high and low, with a particular portion. The high-quality sub-population searches for an optimum solution in an exploitative manner using a movement scheme used in the Rao-3 algorithm. Meanwhile, the low-quality one does in an explorative fashion using a new random walk. Secondly, two evolutionary operators: crossover and mutation, are incorporated to provide both exploitation and exploration strategies. A fitness-based adaptation is introduced to dynamically tune the three parameters: the portion of high-quality individuals, mutation radius, and mutation rate throughout the evolution, based on the improvement of best-so-far fitness. In contrast, the crossover is implemented using a standard random scheme. Comprehensive examinations using 38 benchmarks: twenty-three classic functions, ten CEC-C06 2019 benchmarks, and five global trajectory optimization problems show that the proposed ERA generally outperforms the four competitors: Rao-1, Rao-2, Rao-3, and firefly algorithm with courtship learning (FA-CL). Detailed investigations indicate that both proposed schemes work very well to make ERA evolves in an exploitative manner, which is created by a high portion of high-quality individuals and the crossover operator, and avoids being trapped on the local optimum solutions in an explorative manner, which is generated by a high portion of low-quality individuals and the mutation operator. Finally, the adaptation scheme effectively controls the exploitation-exploration balance by dynamically tuning the portion, mutation radius, and mutation rate throughout the evolution process.

本文提出了一种进化Rao算法（ERA），通过引入两种新方案来增强三种最新的元启发式Rao算法（Rao-1，Rao-2，Rao-3）。首先，根据人口的素质将其分为两个子群体：高人口和低人口，并有特定的比例。高质量子人口使用Rao-3算法中使用的移动方案，以开发方式寻求最佳解决方案。同时，低质量的人使用新的随机游走以探索的方式行事。其次，结合了两个进化算子：交叉和变异，以提供开发和探索策略。引入了基于适应度的适应机制，以动态调整三个参数：整个进化过程中高品质个体的比例，变异半径和变异率，基于迄今为止最好的健身水平的提高。相反，使用标准随机方案来实现交叉。使用38个基准进行的全面检查：二十三个经典功能，十个CEC-C06 2019基准以及五个全局轨迹优化问题表明，拟议的ERA总体上胜过四个竞争对手：Rao-1，Rao-2，Rao-3和萤火虫求爱学习算法（FA-CL）。详细的调查表明，这两种提议的方案都能很好地发挥作用，以使ERA以一种可剥削的方式发展，这是由高素质的高素质人员和跨界运营商创造的，并且避免以探索性的方式陷入局部最优解中，这是由大量劣质个体和变异算子产生的。最后，